Remember that the 1700s was so cold relatively, the soldiers march even in summer with thick jackets and smokepipes.
Though, there was also the introduction of potato, which led to massive demographic explosion in the Protestant Northern Europe.
But I do see your point. Still, the Germanic tribes were the first climate refugees that we know, maybe after the 8.2 kya event [0] that led to the first cities in Fertile Crescent
Not quite. Those germanic tribes were fleeing the huns. The crossing of the danube in 376 by the goths (as war refugees) and the crossing of the rhine in the winter 405/406 by the alans and vandals (as invaders) allowed them to escape the huns. There were extreme climate events recorded in the late antiquity, but that happened more than one century later. For example, https://en.wikipedia.org/wiki/Volcanic_winter_of_536 The Justinian plague occurred 541-549, amplifying the problems of the byzantine empire. Returning to the germans, also in the late antiquity, there is an obscure and unexplained event, in the period 500-550 the vistula and elbe basins were depopulated. Germans migrated from those places or they perished there.
The Roman Warm Period (coming around Caesar era to 400s, explaining the Migration Age) The Medieval Warm Period And the inverse, the Modern Cooling Period (between 1600-1800, if I'm not mistaken).
All three explain macro population movements. Yes, the Germanic tribesmen were climate refugees. So were maybe the European colonists of the New World and other settler colonies.